In this paper,new explicit unidirectional wave solutions for the modified-mixed KdV equation and bidi-rectional waves for the Benjamin Ono equation are studied.New extension of the rational sine-cosine and sinh-cosh m...In this paper,new explicit unidirectional wave solutions for the modified-mixed KdV equation and bidi-rectional waves for the Benjamin Ono equation are studied.New extension of the rational sine-cosine and sinh-cosh methods are used.In addition,an extension of the recent polynomial function method is applied as well.Different types of topological and non-topological soliton solutions are extracted to the proposed models and categorized by providing 2D and 3D graphs.Finally,some physical properties of the new bidirectional waves solutions to the Benjamin Ono model are discussed.展开更多
Smooth support vector machine （SSVM） changs the normal support vector machine （SVM） into the unconstrained op- timization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-G...Smooth support vector machine （SSVM） changs the normal support vector machine （SVM） into the unconstrained op- timization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-Goldfarb-Shanno （BFGS） algorithm and the Newdon-Armijio （NA） algorithm easily, however the accuracy of sigmoid function is not as good as that of polyno- mial smooth function. Furthermore, the method cannot reduce the influence of outliers or noise in dataset. A fuzzy smooth support vector machine （FSSVM） with fuzzy membership and polynomial smooth functions is introduced into the SVM. The fuzzy member- ship considers the contribution rate of each sample to the optimal separating hyperplane and makes the optimization problem more accurate at the inflection point. Those changes play a positive role on trials. The results of the experiments show that those FSSVMs can obtain a better accuracy and consume the shorter time than SSVM and lagrange support vector machine （LSVM）.展开更多
文摘In this paper,new explicit unidirectional wave solutions for the modified-mixed KdV equation and bidi-rectional waves for the Benjamin Ono equation are studied.New extension of the rational sine-cosine and sinh-cosh methods are used.In addition,an extension of the recent polynomial function method is applied as well.Different types of topological and non-topological soliton solutions are extracted to the proposed models and categorized by providing 2D and 3D graphs.Finally,some physical properties of the new bidirectional waves solutions to the Benjamin Ono model are discussed.
基金supported by the National Natural Science Foundation of China (60974082)
文摘Smooth support vector machine （SSVM） changs the normal support vector machine （SVM） into the unconstrained op- timization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-Goldfarb-Shanno （BFGS） algorithm and the Newdon-Armijio （NA） algorithm easily, however the accuracy of sigmoid function is not as good as that of polyno- mial smooth function. Furthermore, the method cannot reduce the influence of outliers or noise in dataset. A fuzzy smooth support vector machine （FSSVM） with fuzzy membership and polynomial smooth functions is introduced into the SVM. The fuzzy member- ship considers the contribution rate of each sample to the optimal separating hyperplane and makes the optimization problem more accurate at the inflection point. Those changes play a positive role on trials. The results of the experiments show that those FSSVMs can obtain a better accuracy and consume the shorter time than SSVM and lagrange support vector machine （LSVM）.
